REQUISITE VARIETY 11/12 



The law of Requisite Variety says that R\s capacity as a regulator 

 cannot exceed R\'i capacity as a channel of communication. 



In the form just given, the law of Requisite Variety can be shown 

 in exact relation to Shannon's Theorem 10, which says that if noise 

 appears in a message, the amount of noise that can be removed by 

 a correction channel is limited to the amount of information that 

 can be carried by that channel. 



Thus, his "noise" corresponds to our "disturbance", his 

 "correction channel" to our "regulator R", and his "message of 

 entropy H" becomes, in our case, a message of entropy zero, for 

 it is constancy that is to be "transmitted". Thus the use of a 

 regulator to achieve homeostasis and the use of a correction channel 

 to suppress noise are homologous. 



Ex. 1 : A certain insect has an optic nerve of a hundred fibres, each of which 

 can carry twenty bits per second; is this sufficient to enable it to defend 

 itself against ten distinct dangers, each of which may, or may not, indepen- 

 dently, be present in each second ? 



Ex. 2: A ship's telegraph from bridge to engine-room can determine one of 

 nine speeds not oftener than one signal in five seconds, and the wheel can 

 determine one of fifty rudder-positions in each second. Since experience 

 has shown that this means of control is normally sufficient for full regulation, 

 estimate a normal upper limit for the disturbances (gusts, traffic, shoals, etc.) 

 that threaten the ship's safety. 



Ex. 3 : A general is opposed by an army of ten divisions, each of which may 

 manoeuvre with a variety of 10^ bits in each day. His intelligence comes 

 through 10 signallers, each of whom can transmit 60 letters per minute for 

 8 hours in each day, in a code that transmits 2 bits per letter. Is his in- 

 telligence-channel sufficient for him to be able to achieve complete regulation? 



Ex. 4: (Continued.) The general can dictate orders at 500 bits/minute for 12 

 hours/day. If his Intelligence were complete, would this verbal channel 

 be sufficient for complete regulation? 



11/12. The diagram of immediate effects given in the previous 

 section is clearly related to the formulation for "directive correla- 

 tion" given by Sommerhoff, who, in his Analytical Biology, uses the 

 diagram 



K 



/ \ 



\ . 



to h h 

 211 



